We show that when a linear quotient map to a separable Banach space X has a Lipschitz right inverse, then it has a linear right inverse. If a separable space X embeds isometrically into a Banach space Y , then Y contains an isometric linear copy of X. This is false for every nonseparable weakly compactly generated Banach space X. Canonical examples of nonseparable Banach spaces which are Lipsch...

We exhibit abelian topological groups admitting no nontrivial strongly continuous irreducible representations in Banach spaces. Among them are some abelian Banach–Lie groups and some monothetic subgroups of the unitary group of a separable Hilbert space.

In this paper we consider perturbation of Xd-Bessel sequences, Xdframes, Banach frames, atomic decompositions and Xd-Riesz bases in separable Banach spaces. Equivalence between some perturbation conditions is investigated.

It is shown that if A is an analytic class of separable Banach spaces with separable dual, then the set A∗ = {Y : ∃X ∈ A with Y ∼= X∗} is analytic. The corresponding result for pre-duals is false.

A Banach space is polyhedral if the unit ball of each of its finite dimensional subspaces is a polyhedron. It is known that a polyhedral Banach space has a separable dual and is c0-saturated, i.e., each closed infinite dimensional subspace contains an isomorph of c0. In this paper, we show that the Orlicz sequence space hM is isomorphic to a polyhedral Banach space if limt→0 M(Kt)/M(t) = ∞ for ...

A projectional skeleton in a Banach space is a σ-directed family of projections onto separable subspaces, covering the entire space. The class of Banach spaces with projectional skeletons is strictly larger than the class of Plichko spaces (i.e. Banach spaces with a countably norming Markushevich basis). We show that every space with a projectional skeleton has a projectional resolution of the ...

For a large class of separable Banach spaces, we prove the real analytic Dolbeault isomorphism theorem for open subsets.